MA8109 Stochastic processes and differential equations

The lecturer this term is Harald Hanche-Olsen.

Lectures are Thursdays and Fridays 10:15–12:00 in room 656, and started on August 20. You can find Øksendal's book on Springerlink. Note that it is freely available only from within the NTNU network. Please respect the copyright and do not distribute the book further.

• Chp. 2
• Chp. 3
• Sec. 4.1–4.2
• Sec. 4.3 ideas and results, no proofs (self-study)
• Sec. 5.1–5.2
• Sec. 5.3 ideas and results, no proofs (self-study)
• Sec. 7.1
• Sec. 7.2 (stop before the proof of Theorem 7.2.4)
• Sec. 7.3
• Sec. 7.4
• Sec. 8.1 (not the proofs of Lemma 8.1.3, 8.1.4 and Theorem 8.1.5)
• Sec. 8.2 (not the proof and not the remark on killing)
• Sec. 8.3 (only Theorem 8.3.1)
• Appendix A
• Appendix B

I have made occassional reference to Evans's book (Lawrence C. Evans: Am introduction to stochastic differential equations), but consider that an aid in understanding rather than curriculum material per se. In particular, I lectured Evans's proof of the Itô formula – but the one in Øksendal's book will do.

Various notes – the ones on measure theory should be considered background material, and are not central in the curriculum:

• Measure And Probability
• Lebesgueintegralet (in Norwegian, unfortunately)
• Martingales and the Itô integral
• Linear SDEs and Physical Brownian Motion
• Informal Comments on Itô Diffusions
• Kolmogorov and Fokker–Planck equations
• Additionally, I wrote an extremely brief note giving a super quick derivation of the abstract Lebesgue integral. It comes in three flavours:
  • For screen viewing (yellow background, variable page length)
  • A5 format (more conventional, also viewable on screens)
  • A4 format (with two A5 pages per sheet, for printing)
• Note on the Lebesgue–Radon–Nikodym theorem (screen/A5/A4)

Here are some exam problems from previous years.